The Standard Model (SM) of particle physics is a very elegant theory that has led to a long list of impressive achievements, one of the latest being the discovery of the Higgs particle. Nowadays, the researchers of the phenomenology at the highest energy frontier face the unknown, and one of the biggest questions in the field is: what physics lies beyond the SM? Progress in answering this question will require the combined efforts of a large number of experimental and theoretical physicists. How does my project fit in this context? The research project that I present will uncover original models describing the laws of physics at the energy frontier; its ultimate goal is to answer: what novel phenomenology may lie beyond the SM? My plan is to attack this question through a constructive approach, and to establish an atlas characterising all the allowed extensions of the SM. In order to achieve this, I will develop a variety of new tools and approaches based on: - the scattering S-matrix bootstrap and positivity constraints, which will permit a rigorous exploration of the space of high energy theories, and the discovery of new exotic effective field theories; - on-shell effective field theory, which will allow us to: a) achieve an unprecedented precision in the determination of observables (key for the interpretation of data from upcoming generations of collider experiments) and b) uncover new hidden structures of the SM; - the Hamiltonian Truncation method, this will be a universal tool for computing quantum field theory observables beyond perturbation theory, providing a window into new strongly-coupled phenomena. Based on my experience and equipped with these new methodologies my team and I will be able to penetrate uncharted territory, and so discover novel phenomenology at the energy frontier, something which is hardly possible with more conventional methods. The approach I propose will be crucial to meet the upcoming challenges in the high energy frontier.